OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 14, ... and the same line from 0, in the direction 0, 42, ..., in the square spiral whose vertices are the generalized 16-gonal numbers. - Omar E. Pol, Oct 03 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 7*n*(n+1) = 14*A000217(n).
G.f.: 14*x/(1-x)^3.
E.g.f.: 7*x*(x + 2)*exp(x). - G. C. Greubel, Aug 02 2017
From Amiram Eldar, Feb 21 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/7.
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/7.
Product_{n>=1} (1 - 1/a(n)) = -(7/Pi)*cos(sqrt(11/7)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (7/Pi)*cos(sqrt(3/7)*Pi/2). (End)
MATHEMATICA
Table[7*n*(n-1), {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
14*Accumulate[Range[0, 50]] (* or *) LinearRecurrence[{3, -3, 1}, {0, 14, 42}, 50] (* Harvey P. Dale, May 11 2021 *)
PROG
(PARI) a(n)=7*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 03 2009
EXTENSIONS
Extended by R. J. Mathar, Aug 06 2009
STATUS
approved